Do NOT listen to anybody saying NOT to put your dog down. OP might be a total moron and the real thing is that the mange is more than what you think.

My hamster had mange. So we paid big money to take this little 30 dollar 3 year lifespan hamster to the veterinary clinic. They shave the hamster of the fur, and tell me to give the hamster, with wicked little teeth, a dip every day. In a week he died anyways.

Weigh the risks for you and choose. Fix it, or adopt it to someone who can, or put it down. Or do the vet and the dip.